Answer:
The volume of the cube is decreasing at a rate of 63.1071 cubic millimeters per minute.
Step-by-step explanation:
The volume of a cube is given by:
[tex]V=s^3[/tex]
Implicitly differentiate the equation with respect to time t:
[tex]\displaystyle \frac{dV}{dt}=3s^2\frac{ds}{dt}[/tex]
The edge of the cube decreases by 0.53 mm/min. Therefore, ds/dt = -0.53.
When the edge is 6.3 mm, s = 6.3.
Substitute and evaluate:
[tex]\displaystyle \frac{dV}{dt}=3(6.3)^2\left(-0.53\right)=-63.1071\text{ mm}^3/\text{min}[/tex]
The volume of the cube is decreasing at a rate of 63.1071 cubic millimeters per minute.
What number is missing here?
2, 3, 5, 8, 13. ?
Answer:
2, 3, 5, 8, 13 missing number is 18.
Choose each of the following that ARE a function
what is the sum of the rational expressions x-4/2x+3x/2x-1
Answer:
May the ans will help you.
please help me please
Answer:
30,000
Step-by-step explanation:
Find the equation (in terms of x ) of the line through the points (-2,5) and (3,4)
y=
Answer:
y = (-1/5)x + 23/5
Step-by-step explanation:
Given:
Two points;
(-2,5) and (3,4)
Find:
Equation of slope
Computation:
y = mx + b
5 = m(-2) + b
5 = -2m + b .......... Eq1
4 = m(3) + b
4 = 3m + b .......... Eq2
Eq2 - Eq1
-1 = 5m
m = -1/5
5 = -2m + b
5 = -2(-1/5) + b
5 = 2/5 + b
b = 23/5
y = mx + b
y = (-1/5)x + 23/5
Select all the numbers that are rational.
Answer:
-14/2 , 1/3 and 0.325 are the rational numbers
Doris has a fish pond 15 by 18 ft. She wants to put grass in a strip of uniform with around the pond. She has enough grass seed for 234 ft squared. How wide will the strip be? Round your answer to the nearest tenth, when appropriate
Check the picture below.
so if we simply subtract the strip area with the pond and the area of the pond only, what's leftover is the area of the strip alone, so
[tex]\stackrel{\textit{area of the grass \underline{with} pond}}{(15+2x)(18+2x)}-\stackrel{\textit{area of the pond}}{(15)(18)}=\stackrel{\textit{their difference}}{232} \\\\\\ 270+30x+16x+4x^2-270=232\implies 46x+4x^2=232 \\\\\\ 23x+2x^2=116\implies 2x^2+23x-116=0[/tex]
[tex]~~~~~~~~~~~~\textit{quadratic formula} \\\\ \stackrel{\stackrel{a}{\downarrow }}{2}x^2\stackrel{\stackrel{b}{\downarrow }}{+23}x\stackrel{\stackrel{c}{\downarrow }}{-116}=0 \qquad \qquad x= \cfrac{ - b \pm \sqrt { b^2 -4 a c}}{2 a} \\\\\\ x = \cfrac{-23\pm \sqrt{23^2-4(2)(-116)}}{2(2)}\implies x = \cfrac{-23\pm \sqrt{1457}}{4}[/tex]
now, the negative root will simply yield a negative value, which is not applicable here, so we'll only use the positive root, since it's the only feasible one for the phenomena
[tex]x = \cfrac{-23+ \sqrt{1457}}{4}\implies x \approx 3.792667341996157\implies \stackrel{\textit{rounded up}}{x = 3.8}[/tex]
Answer:
3 feet
Step-by-step explanation:
Let x be the width of the grass strip.
So the length of the grass strip=18+2x
Area of the grass strip =2(18+2x)(x)+2(15)(x)=2(18x+2x^2)+2(15x)=(36x+4x^2)+30x=4x^2+66x^2
But the available grass seed is enough for 234 ft squared
4x^2+66x=234
4x^2+66x-234=0
x={-66+-[(66)^2–4(4)(-234)]^1/2}/2(4)
x={-66+-[4356+3744]^1/2}/8={-66+-[8100]^1/2}/8
x={-66+-(90)}/8
Two values of x: x=(-66+90)/8=24/8=3 and the other value of x=(-66–90)/8=-19.5. Adopt the positive value of x=3 feet (answer)
So the width of the strip is 3 feet.
Check for the area of grass strip around the fish pond : Area=2(18+6)(3)+2(15)(3)=2(24)(3)+90=144+90=234 square feet
Other area check =4x^2+66x=4(3)^2+66(3)=36+198=234 square feet
Therefore the strip is 3 feet wide
What would be the amount of his last monthly bill in order. The bill amount to be 110 for all 12 months
Question 35 of 49
Which description best describes parallel lines?
A. Lines that are not in the same plane and will never intersect
O B. Lines that intersect at a right angle
O C. Lines that intersect
D. Lines that lie in the same plane but will never intersect
SUBM
Answer:
D.lines that lie in the same plane but will never intersect
Step-by-step explanation:
parallel lie in the same plane but never meet
Which of these strategies would eliminate a variable in the system of equations?
-7x + 2y = 5
3x - 5y = -5
A. Add the equations
B. Multiply the top equation by 3, multiply the bottom equation by 7, then add the equations.
C. Multiply the top equation by 5, multiply the bottom equation by 2, then add the equations.
Answer:
Step-by-step explanation:
A
Given the line segment AB=36 cm and a point C on directed line segment AB that partitions AB into the ratio 1 to 2, find the lengths of the line segments AC and CB
Graph the Image of AKLM after a translation 1 unit left and 7 units up.
9514 1404 393
Answer:
see attached
Step-by-step explanation:
Pick a point (such as K, L, or M). Count one grid square to the left and 7 up. That is its new location.
Simplify: (5x + 3) – (3x – 2)
Answer: 2x+5
Step-by-step explanation:
(5x + 3) – (3x – 2)
5x+3-3x+2
2x+5
Answer:
[tex]\huge\boxed{\boxed{\underline{\textsf{\textbf{Answer}}}}}[/tex]
╭⋟───────────────
[tex](5x+ 3) - (3x - 2) \\ = 5x + 3 - 3x + 2 \\ = 5x - 3x + 3 + 2 \\ = 2x + 5[/tex]
───────────────⋞╯
ʰᵒᵖᵉ ⁱᵗ ʰᵉˡᵖˢ
꧁❣ ʀᴀɪɴʙᴏᴡˢᵃˡᵗ2²2² ࿐
Find the angle measurements of the intersections for the two equations f(x) = 4x - 5 and g(x) = 2x^2 - 5.
Multiple answers
63
7 (This is one of the answers already)
20
76
90
Answer:
76° is the other one
Step-by-step explanation:
nope, no precise calculation here. the option are thankfully enough apart that solving it graphically is just fine. look at the screenshot. the upper intersection is the one with the 7° angle
the lower one is somewhat less than 90° :P
Answer:
76 is the other
Step-by-step explanation:
Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.
Given:
In the given circle, the measure of major arc TV is 220 degrees.
To find:
The measure of angle TUV.
Solution:
In a circle, the measure central angle of arc is equal to its corresponding arc measure and according to central angle theorem, the measure of subtended angle on an arc is half of the measure of central angle of that arc.
So, the measure of subtended angle is half of the measure of its corresponding arc.
[tex]m\angle TUV=\dfrac{1}{2}\times \text{Measure of major arc TV}[/tex]
[tex]m\angle TUV=\dfrac{1}{2}\times 220^\circ[/tex]
[tex]m\angle TUV=110^\circ[/tex]
Therefore, the measure of angle TUV is 110 degrees.
Find the measure of WX and show work
Ans : the measure of WX = 8
Seven times a number decreased by three-fourths of the same number is 25. What is the number?
Answer:
103/28
Step-by-step explanation:
Let the number be 'x'
Equation:-
7x - 3/4 = 25
7x = 25 + 3/4
7x = 100/4 + 3/4
7x = 103/4
x = 103/(4 x 7)
x = 103/28
Answer:
if we make this a algebraic equation it will look like this
7x-3/4x=25
6.25x=25
25 divided by 6.25=4
x=4
to check
28-3=25
Hope This Helps!!!
There are red, blue, and white buttons in a box. The ratio of the
number of red buttons to the number of white buttons is 4:7.
The ratio of the number of blue buttons to the number of red buttons
is 3:2. There are 280 white buttons.
How many buttons are there altogether?
Please help i’m very confused
Answer:
680
Step-by-step explanation:
Ratio of red to white 4 : 7
Number of white = 280
White + red buttons = x
7x / 11 = 280
7x = 280 * 11
7x = 3080
x = 3080 / 7
x = 440
Number of red buttons 440 - 280 = 160
Number of red bottons ;
Blue + red buttons = x
3 : 2 ; blue : red
3 + 2 = 5 ;
2x / 5 = 160
2x = 160 * 5
2x = 800
x = 800 / 2
x = 400
Number of Blue buttons :
400 - 160 = 240
Total :
White + red + blue
280 + 160 + 240 = 680 buttons
2)
110°
18x + 2
A) 8
C) 6
B) 12
D) -10
Answer:
C) 6
Step-by-step explanation:
Alternate interior angles are congruent meaning that they are equal to each other sp 18x+2=110 is simplified to 18x=108. Then divide by 18 to get x equal to 6. Hope this helped and post more :)
Use the table to approximate AB in the triangle below.
Answer:
Answer is 6.1 units
Step-by-step explanation:
The measure of length of AB in the triangle ABC is 6.1 units.
What are trigonometric ratios?The sides and angles of a right-angled triangle are dealt with in Trigonometry. The ratios of acute angles are called trigonometric ratios of angles. The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec).
In the given triangle ABC, BC=5 and ∠A=55°.
We know that, sinθ= Opposite leg length/Hypotenuse length
Here, sinA=BC/AB
sin55°=5/AB
0.82=5/AB
AB=5/0.82
AB=6.1 units
Therefore, the measure of length of AB in the triangle ABC is 6.1 units.
Learn more about the trigonometric ratios here:
brainly.com/question/25122825.
#SPJ2
Consider rolling two fair dice and observing the number of spots on the resulting upward face of each one. Letting A be the event that at least one of the dice results in 6 spots on its upward face, and E be the event that exactly one of the dice results in 6 spots on its upward face, give the value of P(E|A). (Note: This value can be easily obtained by looking at p. 2.3 of the class notes and using a reduced sample space. In fact, such an approach makes the solution so trivial, that for this problem, you don’t have to give any justification for your answer.)
Answer:
[tex]P(E|A)= \frac{10}{11}[/tex]
Step-by-step explanation:
Given
Two rolls of die
[tex]E \to[/tex] one of the outcomes is 6
[tex]A \to[/tex] atleast one is 6
Required
P(E|A)
First, list out the outcome of each
[tex]E = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}[/tex]
[tex]A = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}[/tex]
So:
[tex]P(E|A)= \frac{n(E\ n\ A)}{n(A)}[/tex]
Where:
[tex]E\ n\ A = \{(1,6),(2,6),(3,6),(4,6),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5)\}[/tex]
[tex]n(E\ n\ A) = 10[/tex]
[tex]n(A) = 11[/tex]
So:
[tex]P(E|A)= \frac{10}{11}[/tex]
cos() =
O A. V
B.
173
2
OC.
OD.
-3
Answer:
-√3/2
Step-by-step explanation:
Given the expression:
Cos(7π/6)
Conver to degrees
= Cos(7(180)/6)
= cos 210
= -√3/2
Hence the value of cos(7π/6) is -√3/2
A city is designing a new trail system that will be
6 1/6 miles long. They plan on placing 49 mileage signs to show the distance. How far apart will each sign be?
Step-by-step explanation:
the answer is 6.125 and its will be divided by 125
You roll a die with the sample space s=1,2,3,4,5,6. you define A as (1,2,4) B as (2,3,4,5,6) C as (3,4) and D as (2,4,5). Determine which of the following events are exhaustive and/or mutually exhaustive.
Exhaustive Mutually exclusive
A and B
A and C
A and D
Band C
Answer:
A and B are exhaustive.
Step-by-step explanation:
Given
[tex]A = \{1,2,4\}[/tex]
[tex]B = \{2,3,4,5,6\}[/tex]
[tex]C =\{3,4\}[/tex]
[tex]D = \{2,4,5\}[/tex]
Solving (a): The mutually exclusive events
These are events that have no common or mutual elements
Events A to D are not mutually exclusive because each of the events have at least 1 common element with one another.
Solving (b): Exhaustive events.
Two events X and Y are said to be exhaustive if:
[tex]S = P(X\ n\ Y)[/tex]
i.e. if the sample space equals the intersection of X and Y
For events A to D, we have:
[tex]A\ n\ B = \{1,2,3,4,5,6\}[/tex]
and the sample space is:
[tex]S = \{1,2,3,4,5,6\}[/tex]
By comparison;
[tex]A\ n\ B = S[/tex]
Hence, A and B are exhaustive.
Please help please guys how are you doing
Answer:
the answer of the the triangle is 6
Answer:
6
Step-by-step explanation:
First row:
8 ÷ 2 = 4. → Square: 4
Second row:
14 - 4 = 10.
[two circles] = 10. So, 10÷2 = 5.
Circle = 5
Third Row:
[triangle] + 5 = 11
11 - 5 = 6
Triangle = 6
How should I tell my crush I like her? She's my friend and I asked her if she liked me yesterday and she said no but I think she was lying because she typed and then stoped typing and said no
Answer:
U just have to make her feel comfortable to trust u that she can tell u that she actually likes u....dont push anything just make her feel appreciated ok?
Step-by-step explanation:
that's all
A health clinic dietician is planning a meal consisting of three foods whose ingredients are summarized as follows: One Unit ofFood I Food II Food IIIUnits of Protein 10 15 20Units of Carbohydrates 1 2 1Units of Iron 4 8 11Calories 80 120 100The dietician wishes to determine the number of units of each food to use to create a balanced meal containing at least 40 units of protein, 6 units of carbohydrates, and 12 units of iron, and with as few calories as possible. Use solver to find how many units of each food should be used in order to minimize calories.
Answer:
z (min) = 360 x₁ = x₃ = 0 x₂ = 3
Step-by-step explanation:
Protein Carbohydrates Iron calories
Food 1 (x₁) 10 1 4 80
Food 2 (x₂) 15 2 8 120
Food 3 (x₃) 20 1 11 100
Requirements 40 6 12
From the table we get
Objective Function z :
z = 80*x₁ + 120*x₂ + 100*x₃ to minimize
Subjet to:
Constraint 1. at least 40 U of protein
10*x₁ + 15*x₂ + 20*x₃ ≥ 40
Constraint 2. at least 6 U of carbohydrates
1*x₁ + 2*x₂ + 1*x₃ ≥ 6
Constraint 3. at least 12 U of Iron
4*x₁ + 8*x₂ + 11*x₃ ≥ 12
General constraints:
x₁ ≥ 0 x₂ ≥ 0 x₃ ≥ 0 all integers
With the help of an on-line solver after 6 iterations the optimal solution is:
z (min) = 360 x₁ = x₃ = 0 x₂ = 3
At the end of a snowstorm, Jamal had 18 inches of snow on his lawn. The temperature then increased and the snow began to melt at a constant rate of 2.5 inches per hour. Assuming no more snow was falling, how much snow would Jamal have on his lawn 5 hours after the snow began to melt? How much snow would Jamal have on his lawn after tt hours of snow melting?
Answer:
Part 1)
5.5 inches.
Part 2)
[tex]y=-2.5t+18[/tex]
Step-by-step explanation:
We can write a linear equation to model the function.
Let y represent the inches of snow and let t represent the number of hours since the end of the snowstorm.
A linear equation is in the form:
[tex]y=mt+b[/tex]
Since there was 18 inches of snow in the beginning, our y-intercept or b is 18.
Since it melts at a constant rate of 2.5 inches per hour, our slope or m is -2.5.
Substitute:
[tex]y=-2.5t+18[/tex]
This equation models how much snow Jamal will have on his lawn after t hours of snow melting.
So, after five hours, t = 5. Substitute and evaluate:
[tex]y=-2.5(5)+18=5.5\text{ inches}[/tex]
After five hours, there will still be 5.5 inches of snow.
Find two consecutive integers whose sum is 901.
the answer is :
x+1 and x+2
Answer:
900+1=901
Step-by-step explanation:
Nadia has $1.35 in nickels. How many nickels
does she have?
Answer:
27 Nickels
Step-by-step explanation:
Divide 1.35 by 0.05
= 27